Question

If the following pair of the triangle is congruent? state the condition of congruency: 

In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.

Answer 1

In ΔPQR

∠R = 40°, ∠Q = 50°

∠P + ∠Q + ∠R = 180°        ...[Sum of all the angels in aa triangle = 180°]

⇒ ∠P + 50° + 40° = 180°  

⇒ ∠P + 90° = 180°   

⇒ ∠P = 180° - 90° 

⇒ ∠P = 90°  

In ΔABC and ΔPQR

∠A = ∠P

∠C = ∠R

BC = QR  

By Angle-Angle-Side criterion of congruency, the triangles

ΔABC and ΔPQR are congruent to each other.

∴ ΔABC ≅ ΔPQR